וַיִּֽתְחַטְּא֣וּ הַלְוִיִּ֗ם וַֽיְכַבְּסוּ֙ בִּגְדֵיהֶ֔ם וַיָּ֨נֶף אַהֲרֹ֥ן אֹתָ֛ם תְּנוּפָ֖ה לִפְנֵ֣י יְהוָ֑ה וַיְכַפֵּ֧ר עֲלֵיהֶ֛ם אַהֲרֹ֖ן לְטַהֲרָֽם׃
И очистили себя левиты и отмыли одежду свою; и Аарон принес их за священный дар пред Господом; и Аарон искупил их, чтобы очистить их.
Rashbam
ויתחטאו, as per the instruction in verse 7:הזה עליהם מי חטאת, “sprinkle on them of the waters containing the ash of the read heifer.”
Chizkuni
ויתחטאו הלוים, “the Levites purified themselves.” They did so by means of sprinkling the waters containing the ash of the red heifer upon themselves.
Tur HaArokh
וינף אהרן אותם תנופה...ויכפר עליהם, “Aaron performed a waving motion with each of them,…..and he provided atonement for them.” Ibn Ezra again explains that at that stage the atonement had already been provided for them. [The steps leading to their atonement had already been described in the previous verse. Ed.]